Question

olve the following using the various principles together. Don't forget to check. 2/3 x 7/8+4t-1/8=7/8

Answer 1

To solve the equation 2/3 x 7/8 + 4t - 1/8 = 7/8, we need to eliminate terms and simplify the algebra. First, we multiply the fractions to get 14/24. Then, we combine like terms and solve for t to find the solution of t = 116/576.

Step-by-step explanation:

To solve the equation 2/3 x 7/8 + 4t - 1/8 = 7/8, we need to eliminate terms and simplify the algebra.

First, we multiply the fractions: (2/3) x (7/8) = 14/24.

Next, we simplify the equation: 14/24 + 4t - 1/8 = 7/8. To make the terms have a common denominator, we multiply 14/24 by 1/3 to get 14/72. So the equation becomes: 14/72 + 4t - 1/8 = 7/8.

Now, we can combine like terms by adding and subtracting fractions: 14/72 - 1/8 = (7/8) - (4t). To make the fractions have a common denominator, we find the least common multiple of 72 and 8, which is 72. So the equation becomes: 14/72 - 9/72 = (7/8) - (4t).

Simplifying the fractions on both sides of the equation, we get: 5/72 = (7/8) - (4t).

Now, we can solve for t by isolating the variable:

5/72 + (4t) = 7/8.

To get rid of the fraction on the left side, we multiply 5/72 by 8/8 to get 40/576. So the equation becomes: 40/576 + (4t) = 7/8.

Next, we subtract 40/576 from both sides: (4t) = 7/8 - 40/576.

To subtract fractions, we need a common denominator. The least common multiple of 8 and 576 is 576, so the equation becomes: (4t) = 504/576 - 40/576.

Now we can subtract the fractions: (4t) = 464/576.

Finally, to solve for t, we divide both sides by 4: (t) = (464/576) / 4.

Dividing the fractions, we get: (t) = (464/576) * (1/4) = 116/576.

So the solution to the equation is: t = 116/576.

To check the solution, we can substitute t = 116/576 back into the original equation and see if it equals 7/8.

Formatted Answer:

1. Multiply the fractions: (2/3) x (7/8) = 14/24.
2. Simplify the equation: 14/24 + 4t - 1/8 = 7/8.
3. Combine like terms by adding and subtracting fractions: 14/72 - 1/8 = (7/8) - (4t).
4. Solve for t by isolating the variable: 5/72 = (7/8) - (4t).
5. Get rid of the fraction on the left side: 5/72 + (4t) = 7/8.
6. Subtract 40/576 from both sides: (4t) = 7/8 - 40/576.
7. Subtract fractions to get a common denominator: (4t) = 464/576.
8. Divide both sides by 4 to solve for t: (t) = 116/576.